Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement of the Quadrature of the Circle and the Geometry of SolidsF. Nichols, 1806 - 311 sider |
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Side 19
... manner , it may be demonstrated , that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. PROP . XV . THEOR . IF two straight ...
... manner , it may be demonstrated , that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. PROP . XV . THEOR . IF two straight ...
Side 20
... manner , if the side BC Be bisected , it may be demonstrated that the angle BCG , that is the angle ACD , is greater than the angle ABC . Therefore , if one side , & c . Q. E. D. PROP . XVII . THEOR . ANY two angles of a triangle are ...
... manner , if the side BC Be bisected , it may be demonstrated that the angle BCG , that is the angle ACD , is greater than the angle ABC . Therefore , if one side , & c . Q. E. D. PROP . XVII . THEOR . ANY two angles of a triangle are ...
Side 21
... manner , it may be demonstrated , that BAC , ACB , as also CAB , ABC , are less than two right angles . Therefore , any two angles , & c . Q. E. D. PROP . XVIII . THEOR . THE greater side of every triangle has the greater angle opposite ...
... manner , it may be demonstrated , that BAC , ACB , as also CAB , ABC , are less than two right angles . Therefore , any two angles , & c . Q. E. D. PROP . XVIII . THEOR . THE greater side of every triangle has the greater angle opposite ...
Side 23
... manner it may be demonstrated , that the sides AB , BC are greater than CA , and BC , CA greater than AB . Therefore any two sides , & c . Q. E. D. PROP . XXI . THEOR . IF from the ends of one side of a triangle there N. be drawn two ...
... manner it may be demonstrated , that the sides AB , BC are greater than CA , and BC , CA greater than AB . Therefore any two sides , & c . Q. E. D. PROP . XXI . THEOR . IF from the ends of one side of a triangle there N. be drawn two ...
Side 29
... manner it may be de- c monstrated that they do not meet towards A , C ; but those straight lines which meet neither way , though produced ever so far , are parallel to one another . AB therefore is parallel b 30. Def . to CD . Wherefore ...
... manner it may be de- c monstrated that they do not meet towards A , C ; but those straight lines which meet neither way , though produced ever so far , are parallel to one another . AB therefore is parallel b 30. Def . to CD . Wherefore ...
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Almindelige termer og sætninger
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle contained angle EDF arch base BC bisected Book centre circle ABC circumference coincide cylinder definition demonstrated diameter draw drawa equal angles equiangular equilateral polygon equimultiples Euclid exterior angle fore four right angles given circle given straight line greater inscribed interior and opposite join less Let ABC Let the straight meet multiple opposite angle parallelogram perpendicular point F polygon prism PROB produced proportional proposition pyramid Q. E. D. COR Q. E. D. PROP ratio rectangle contained rectilineal figure remaining angle segment solid angle solid parallelepipeds straight line AB straight line AC Suppl THEOR third touches the circle triangle ABC triangle DEF
Populære passager
Side 121 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Side 42 - TO a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Side 63 - Therefore, in obtuse-angled triangles, &c. QED PROP. XIII. THEOREM. In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
Side 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 183 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF is the same with the ratio which is compounded •f the ratios of their sides.
Side 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 291 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Side 160 - ... extremities of the base shall have the same ratio which the other sides of the triangle have to one...
Side 10 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.
Side 14 - Therefore, upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extretnity equal to one another.
Bibliografiske oplysninger
| Titel | Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement of the Quadrature of the Circle and the Geometry of Solids |
| Forfatter | John Playfair |
| Udgiver | F. Nichols, 1806 |
| Oprindeligt fra | University of Michigan |
| Digitaliseret | 16. feb 2008 |
| ISBN | 0608378402, 9780608378404 |
| Længde | 311 sider |
| Eksporter henvisning | BiBTeX EndNote RefMan |